97-06-01.ley-wh
The automatic generation of one- and multi-dimensional
distributions with transformed density rejection
Abstract
A rejection algorithm, called ``transformed density rejection'', is
presented. It uses a new method for constructing simple hat functions
for a unimodal density $f$. It is based on the idea of transforming $f$
with a suitable transformation $T$ such that $T(f(x))$ is concave. The
hat function is then constructed by taking the pointwise minimum of
tangents which are transformed back to the original scale.
The resulting algorithm works very well for a
large class of distributions and is fast.
The method is also extended to the two- and multidimensional case.
Mathematics Subject Classification:
65C10 (Random Number Generation)
CR Categories and Subject Descriptors:
G.3 [Probability and Statistics]: Random number generation
General Terms:
Algorithms
Key Words:
random number generation, rejection method, log-concave density
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Josef.Leydold@statistik.wu-wien.ac.at